Statistical Plant Set Estimation using Schroeder-Phased Multisinusoidal Input Design

In this paper, a frequency domain method is developed for plant set estimation. The estimation of a plant "set" rather than a point estimate is required to support many methods of modern robust control design. The approach here is based on using a Schroeder-phased multisinusoid input design which has the special property of placing input energy only at the discrete frequency points used in the computation. A detailed analysis of the statistical properties of the frequency domain estimator is given leading to exact expressions for the probability distribution of the estimation error, and many important properties. It is shown that for any nominal parametric plant estimate, one can use these results to construct an overbound on the additive uncertainty to any prescribed statistical confidence. The "soft" bound thus obtained can be used to replace "hard" bounds presently used in many robust control analysis and synthesis methods.